Metastability in the diluted parallel Ising model

TL;DR

This paper investigates the effects of parallel implementation and dilution on the metastability and phase transitions in the kinetic Ising model, revealing how asynchronism influences symmetry breaking and phase coexistence.

Contribution

It introduces the concept of dilution to induce phase transitions and metastability in the parallel kinetic Ising model, highlighting the impact of asynchronism on equilibrium behavior.

Findings

Dilution induces transitions between homogeneous and checkerboard phases.

Parallel implementation can suppress symmetry breaking at low temperatures.

Metastable transients are observed due to asynchronism.

Abstract

We present some considerations about the parallel implementations of the kinetic (Monte Carlo) version of the Ising model. In some cases the equilibrium distribution of the parallel version does not present the symmetry breaking phenomenon in the low-temperature phase, i.e., the stochastic trajectory originated by the Monte Carlo simulation can jump between the distributions corresponding to both kinds of magnetization, or the lattice can break into two disjoint sublattices, each of which goes into a different asymptotic distribution (phase). In this latter case, by introducing a small asynchronism (dilution), we can have a transition between the homogeneous and the checkerboard phases, with metastable transients.